Methods and apparatus for optimizing an electrical response to a set of conductive layers on a substrate

ABSTRACT

A method of determining a first thickness of a first conductive layer formed of a first conductive material on a target substrate, the target substrate further having a second conductive layer formed of a second conductive material different from the first conductive material, is disclosed. The method includes positioning a first eddy current sensor at a given position relative to the target substrate, the first eddy current sensor being in a spaced-apart relationship with respect to the target substrate when positioned at the given position. The method also includes measuring, using the first eddy current sensor while the first eddy current sensor is positioned at the give position, a first set of electrical responses that includes at least one of a first voltage measurement and a first current measurement, the measuring the first set of electrical responses being performed at a first target substrate temperature. The method further includes measuring, using the first eddy current sensor while the first eddy current sensor is positioned at the given position, a second set of electrical responses that includes at least one of a second voltage measurement and a second current measurement, the measuring the second set of electrical responses being performed at a second target substrate temperature different from the first target substrate temperature. The method also includes calculating a third set of electrical responses using at least the first set of electrical responses and the second set of electrical responses, and a first temperature coefficient of the first conductive layer, the third set of electrical responses representing responses substantially attributable to the first conductive layer; and determining the first thickness from the third set of electrical responses.

BACKGROUND OF THE INVENTION

The present invention relates in general to substrate manufacturingtechnologies and in particular to methods and apparatus for optimizingan electrical response to a set of conductive layers on a substrate.

In the processing of a substrate, e.g., a semiconductor wafer, MEMSdevice, or a glass panel such as one used in flat panel displaymanufacturing, plasma is often employed. As part of the processing of asubstrate (chemical vapor deposition, plasma enhanced chemical vapordeposition, physical vapor deposition, etc.) for example, the substrateis divided into a plurality of dies, or rectangular areas, each of whichwill become an integrated circuit. The substrate is then processed in aseries of steps in which materials are selectively removed (etching) anddeposited (deposition) in order to form electrical components thereon.

Metals are particularly important materials in substrate manufacturing.For example, in a manufacturing method, known as dual damascene,dielectric layers are electrically connected by a conductive plugfilling a via hole. Generally, an opening is formed in a dielectriclayer, usually lined with a TaN or TiN barrier, and then subsequentlyfilled with other conductive material (e.g., aluminum (Al), copper (Cu),tungsten (W), etc.) that allows electrical contact between two sets ofconductive patterns. This establishes electrical contact between twoactive regions on the substrate, such as a source/drain region. Excessconductive material on the surface of the dielectric layer is typicallyremoved by chemical mechanical polishing (CMP). A blanket layer ofsilicon nitride or silicon carbide may then be deposited to cap thecopper.

Subsequently, in order to insure that the process is within acceptableparameters, it is often important to determine the electrical film/layerproperties (e.g., thickness, sheet resistance, etc.) of a conductivelayer at a particular point on the substrate. One method of measurementis the use of eddy current sensors. Generally, eddy currents arecurrents that are induced in a conductive media by an alternatingmagnetic field.

In general, if a first alternating current is applied to a wire wrappedin a generally solenoidal shape (e.g., the wire in an eddy currentsensor), a first alternating electromagnetic field forms in and aroundthe solenoid extending beyond the ends of the solenoid a distance on theorder of the diameter of the solenoid. If this first field is broughtinto proximity with a second conductor (e.g., a conductive layer on thesubstrate) a second alternating electrical current will also flow in thesecond conductor, causing a second field that interacts with (e.g., addsvectorally to) the first field and results in a perturbation to thefield around the probe. These perturbations in the probe's initial fieldmay cause detectable changes in the probe's electrical characteristicsincluding the probe's impedance and frequency response. Using animpedance-voltage converter, the impedance change can be converted intoa voltage change for further signal processing and analysis.

Many techniques are available for producing a signal from these detecteddifferences in eddy current probe characteristics. For example, in afirst technique, the width of the frequency dependent power absorptionof the probe/eddy current sensor system (sensor system) can be reported.Likewise, in a second technique, the change in the magnitudes of thereal and/or imaginary parts of the probe impedance can be reportedbetween the probe and the second conductor. These measurements aregenerally made using passive or active circuitry to produce a range ofvoltages that can be bounded by the signal with no second conductorpresent and the signal with a second conductor causing maximal change inthe signal. The exact shape, thickness and conductivity of the secondconductor that causes the maximal change in the probe signal generallydepends on the probe geometry, excitation frequency and the methodadopted for measurement, but generally it is a thick (on the order ofmany times the diameter of the probe) conductive film (layer) placed asnear to the probe as possible.

Depending on the application, conductive or magnetic elements can alsobe incorporated into the design of the probe in order to modify thespatial extent and magnitude of the probe field and hence the spatialand electrical sensitivity to the second conductive layer. For optimumperformance, the sensor system should maximize sensor system sensitivityto the desired electrical property of the conductive film (e.g.,thickness, sheet resistance, etc.) while minimizing the sensor system'ssensitivity to all other effects and variables.

Generally, the electrical response of sensor to the magnetic field (eddycurrent perturbations), and hence its accuracy, is affected by theproximity (substrate proximity response) of the sensor to the substrate.That is, as the exciting probe field is of limited spatial extent andits magnitude decreases as the position increases from the probe, theoverall eddy current perturbations caused by a second conductor beingmeasured also decrease as the second conductor is moved further from theprobe. Thus, an eddy current sensor may be sensitive to both proximityand electrical film properties. In general, it is difficult to isolatethe portion of the electrical response caused by the set of electricalfilm properties (electrical film property response) from the portion ofthe electrical response caused by proximity (substrate proximityresponse), which may subsequently introduce an error in the reportedvalue.

In addition, the set of electrical film properties for a particularsubstrate may itself be variable. For example, the electrical responseof sensor may be affected by the resistivity of the conductive film.That is, eddy current signal variation is primarily proportional to theinverse of film resistivity. Electrical resistivity (also known asspecific electrical resistance) generally indicates how strongly amaterial opposes the flow of electric current. A low resistivitygenerally indicates a material that readily allows the movement ofelectrons. However, resistivity is also generally dependent ontemperature.

Referring now to FIG. 1, a simplified diagram of an eddy current sensoris shown. Generally, changes in the sensor's coil impedance 102 arecaused by varying the distance 104 between the sensor (coil) andsubstrate 106. Since the electrical parameters of target materialresistivity and permeability may determine the magnitude of the measuredsensor perturbation, the sensor system is generally calibrated for thetarget material.

One solution to improve the response of a given sensor may be to averageout the proximity errors of multiple sensors, each concurrently tryingto measure the same point on the substrate from the same proximity(e.g., concurrent multiple sensors). For example, two sensors, each witha known and fixed proximity to each other, may be positioned at a fixedproximity to a conductive layer positioned between them. In a commonimplementation, one sensor is positioned above the substrate and theother sensor is positioned below the substrate. If each sensor has asubstantially identical sensitivity to proximity, the electricalresponse on any one sensor may be substantially equal but opposite tothe electrical response on the other sensor. Subsequently, averagingtogether a signal from each sensor may result in a combined signal thatis much less sensitive to the position (proximity) of the conductivelayer to either one of the two sensors, and which subsequently may beused to better report the desired electrical property of the conductivefilm (e.g., more independent of proximity).

By periodically calibrating the sensor system (sensors, substrategeometry and substrate handling, stage movements, etc.) prior to makingmeasurements, the proximity error in theory may be cancelled out byaveraging a pair of measurements taken when the substrate is placed inthe known position between the sensors. In practice, however, it isoften very difficult to repeatably and precisely position the eddycurrent sensors with respect to the measured conductive layer.

For example, the equipment used to position a substrate between sensorsmay have a tolerance range that is too broad, so that the perturbationsof the sensors due to changes in the substrate film thickness aresubstantially similar when compared to the sensor perturbations measureddue the differing proximities at different measurement placements ortimes. Likewise, a mechanism used to move the substrate with respect tothe sensors (i.e., turntable, etc.) may induce vibrations in thesubstrate or changes in the substrate proximity with amplitudes thatcause perturbations in probe signals that exceed the measureddifferences in film thickness or introduce uncertainty in the reportedfilm thickness in excess of the desired precision for the sensor system.Subsequently, even relatively small proximity variations may introducesubstantial errors in the measurements, presenting a problem for highprecision measurements, such as substrate manufacturing.

In addition, even if the proximity error for concurrent multiple sensorscould be substantially minimized, it may still be desirable to make themeasurements at different points in time (e.g., sequential measurement).For example, since sensors are often located on a sensor swing arm, itmay be inconvenient to align both sensors when moving the sensor swingarm across the surface of the substrate. That is, two sensors may beplaced on the sensor swing arm such that they form a line parallel to avector that is tangent to the rotation of the substrate on a turntable.As the sensor arm swings across the rotating substrate, the anglebetween the sensor line and the tangent vector may increase to the pointat which both sensors cannot be positioned over the same point on thesubstrate at the same time. Additionally, the sensor swing armconstruction itself may prevent locating the sensors on top of eachother, or interference from one sensor (e.g., cross talk) may preventthe simultaneous use of both sensors.

Referring now to FIG. 2, a simplified diagram of a substrate in amechanism to rotate it with a sensor arm is shown. In this example,substrate 202 rotates in direction 208, as sensor swing arm 204 movessensors 206 across the surface of substrate 202.

In view of the foregoing, there are desired methods and apparatus foroptimizing an electrical response to a set of conductive layers on asubstrate.

SUMMARY OF THE INVENTION

The invention relates, in one embodiment, to a method of determining afirst thickness of a first conductive layer formed of a first conductivematerial on a target substrate, the target substrate further having asecond conductive layer formed of a second conductive material differentfrom the first conductive material. The method includes positioning afirst eddy current sensor at a given position relative to the targetsubstrate, the first eddy current sensor being in a spaced-apartrelationship with respect to the target substrate when positioned at thegiven position. The method also includes measuring, using the first eddycurrent sensor while the first eddy current sensor is positioned at thegive position, a first set of electrical responses that includes atleast one of a first voltage measurement and a first currentmeasurement, the measuring the first set of electrical responses beingperformed at a first target substrate temperature. The method furtherincludes measuring, using the first eddy current sensor while the firsteddy current sensor is positioned at the given position, a second set ofelectrical responses that includes at least one of a second voltagemeasurement and a second current measurement, the measuring the secondset of electrical responses being performed at a second target substratetemperature different from the first target substrate temperature. Themethod also includes calculating a third set of electrical responsesusing at least the first set of electrical responses and the second setof electrical responses, and a first temperature coefficient of thefirst conductive layer, the third set of electrical responsesrepresenting responses substantially attributable to the firstconductive layer; and determining the first thickness from the third setof electrical responses.

The invention relates, in another embodiment, to an arrangement fordetermining a first thickness of a first conductive layer formed of afirst conductive material on a target substrate, the target substratefurther having a second conductive layer formed of a second conductivematerial different from the first conductive material. The arrangementincludes an eddy current sensor disposed at a given position relative tothe target substrate, the first eddy current sensor being in aspaced-apart relationship with respect to the target substrate when thefirst eddy current sensor is positioned at the given position. Thearrangement also includes means for storing a first set of electricalresponses, the first set of electrical responses being measured usingthe first eddy current sensor while the first eddy current sensor ispositioned at the given position, the first set of electrical responsesbeing measured at a first target substrate temperature. The arrangementfurther includes means for storing a second set of electrical responses,the second set of electrical responses being measured using the firsteddy current sensor while the first eddy current sensor is positioned atthe given position, the second set of electrical responses beingmeasured at a second target substrate temperature different from thefirst target substrate temperature. The arrangement also includes meansfor calculating a third set of electrical responses using at least thefirst set of electrical responses and the second set of electricalresponses, and a first temperature coefficient of the first conductivelayer, the third set of electrical responses representing responsessubstantially attributable to the first conductive layer; and means fordetermining the first thickness from the third set of electricalresponses.

The invention relates, in another embodiment, to a method of determininga first thickness of a first conductive layer formed of a firstconductive material on a target substrate, the target substrate furtherhaving at least a second conductive layer formed of a second conductivematerial different from the first conductive material. The methodincludes measuring, using an eddy current sensor disposed proximate tothe substrate, at least two sets of electrical responses at twodifferent target substrate temperatures. The method also includescalculating a layer-specific set of electrical responses from the atleast two sets of electrical responses, the layer-specific set ofelectrical responses, the layer-specific set of electrical responsesrepresenting responses substantially attributable to the firstconductive layer; and determining the thickness from the layer-specificset of electrical responses.

These and other features of the present invention will be described inmore detail below in the detailed description of the invention and inconjunction with the following figures.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is illustrated by way of example, and not by wayof limitation, in the figures of the accompanying drawings and in whichlike reference numerals refer to similar elements and in which:

FIG. 1 illustrates a simplified diagram of an eddy current sensor;

FIG. 2 illustrates a simplified diagram of a substrate on a turntablewith a sensor arm;

FIG. 3 illustrates a set of three calibration curves for determining thethickness of a conductive layer on a substrate, according to oneembodiment of the invention;

FIG. 4 illustrates a simplified diagram of a substrate with a conductivefilm comprising Cu, cycled between about 21° C. and about 23 ° C. across90 minutes, according to an embodiment of the invention;

FIG. 5 illustrates a simplified diagram of a substrate with a conductivefilm comprising Si, cycled between about 21° C. and about 23° C. across90 minutes, according to an embodiment of the invention;

FIG. 6 illustrates a simplified diagram comparing temperaturecoefficient α to substrate mean thickness for a conductive filmsubstantially comprising Cu, according to an embodiment of theinvention; and,

FIG. 7 illustrates a simplified diagram of a method of determining athickness of a first conductive layer on a target substrate, the targetsubstrate further having a second conductive layer, according to anembodiment of the invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention will now be described in detail with reference toa few preferred embodiments thereof as illustrated in the accompanyingdrawings. In the following description, numerous specific details areset forth in order to provide a thorough understanding of the presentinvention. It will be apparent, however, to one skilled in the art, thatthe present invention may be practiced without some or all of thesespecific details. In other instances, well known process steps and/orstructures have not been described in detail in order to notunnecessarily obscure the present invention.

While not wishing to be bound by theory, it is believed by the inventorherein that variations in substrate electrical film properties may becompensated for, in order to optimize sensor electrical response. In anembodiment, a sensor electrical response of a reference substrate sampleat a known temperature may be used to correct the sensor electricalresponse of a target subtrate at an unknown temperature. In anembodiment, the conductive layer material of the reference substrate issubstantially similar to the conductive layer material of the targetsubstrate.

In an embodiment, the reference substrate and the target substrate aremeasured using substantially similar measurement protocols. For example,both the reference substrate and the target substrate may be measuredusing the same eddy current measurement technique, at about the sameproximity, and at about the same measurement sites (geometry), etc.,such that the major variable between the reference substrate and thetarget substrate is temperature. In an embodiment, if the substrate hastwo conductive films with differing resistivity temperaturecoefficients, a set of measurements may be taken at differenttemperatures in order to derive a substantially temperature independentvalue of a desired film thickness.

Various embodiments are described hereinbelow, including methods andtechniques. It should be kept in mind that the invention may also coverarticles of manufacture that includes a computer readable medium onwhich computer-readable instructions for carrying out embodiments of theinventive technique are stored. The computer readable medium mayinclude, for example, semiconductor, magnetic, opto-magnetic, optical,or other forms of computer readable medium for storing computer readablecode. Further, the invention may also cover apparatuses for practicingembodiments of the invention. Such apparatus may include circuits,dedicated and/or programmable, to carry out tasks pertaining toembodiments of the invention. Examples of such apparatus include ageneral purpose computer and/or a dedicated computing device whenappropriately programmed and may include a combination of acomputer/computing device and dedicated/programmable circuits adaptedfor the various tasks pertaining to embodiments of the invention.Examples of such apparatus may include appropriate dedicated and/orprogrammable circuitry in one or more integrated circuits configured tocarry out the computer-implemented techniques disclosed herein. Inaddition, and in general, for any calculation using a computer, operandsin memory or computer registers are required.

As previously stated, the electrical response of sensor to the magneticfield (eddy current perturbations), and hence its accuracy, is affectedby the proximity (substrate proximity response) of the sensor to thesubstrate. That is, as the exciting probe field is of limited spatialextent and its magnitude decreases as the position increases from theprobe, the overall eddy current perturbations caused by a secondconductor being measured also decrease as the second conductor is movedfurther from the probe. Thus, an eddy current sensor may be sensitive toboth proximity and electrical film properties. In general, it isdifficult to isolate the portion of the electrical response caused bythe set of electrical film properties (electrical film propertyresponse) from the portion of the electrical response caused byproximity (substrate proximity response), which may subsequentlyintroduce an error in the reported value.

In addition, the set of electrical film properties for a particularsubstrate may itself be variable. For example, the electrical responseof sensor may be affected by the resistivity of the conductive film.That is, eddy current signal variation is primarily proportional to theinverse of film resistivity. Electrical resistivity (also known asspecific electrical resistance) generally indicates how strongly amaterial opposes the flow of electric current. A low resistivitygenerally indicates a material that readily allows the movement ofelectrons. However, resistivity is also generally dependent ontemperature.

In general, each sensor response, R, can be modeled as a function ofseveral key variablesR(−)=R(d,p,S,ρ(T))   [EQUATION 1]where d is film thickness to be measured, p is proximity and S isgenerally the sensor serial number which is a short hand notationdenoting the functional dependence of the response on all theinformation about the conversion of the detected perturbation of theparticular eddy current probe's field by the measured film into aconvenient measurement unit, and p(T) is the temperature dependentresistivity. In an embodiment, the convenient measurement unit is volts(V). Assuming that all sensors have the same sensor serial number,EQUATION 1 may be further simplified to:R(−)=R(d, p, ρ(T))   [EQUATION 2]Therefore, the thickness d of a conductive film on the substrate may bemodeled as:d=f(R(d, p, ρ(T)))   [EQUATION 3]

Electrical resistivity (also known as specific electrical resistance) isgenerally indicates how strongly a material opposes the flow of electriccurrent. A low resistivity generally indicates a material that readilyallows the movement of electrons. The SI unit for electrical resistivityis the ohm meter. The electrical resistivity of a material is usuallygiven by $\begin{matrix}{\rho = \frac{RA}{l}} & \left\lbrack {{EQUATION}\quad 4} \right\rbrack\end{matrix}$where ρ is the electrical resistivity (measured in ohm meters), R is theresistance of a uniform specimen of the material (measured in ohms), Iis the length of the specimen (measured in meters), and A is thecross-sectional area of the specimen (measured in square meters).

Electrical resistivity can also be defined as: $\begin{matrix}{\rho = \frac{E}{J}} & \left\lbrack {{EQUATION}\quad 5} \right\rbrack\end{matrix}$where E is the magnitude of the electric field (measured in volts permeter) and J is the magnitude of the current density (measured inamperes per square meter).

Referring now to FIG. 3, a set of three calibration curves at aparticular substrate temperature (calibration temperature) fordetermining the thickness of a conductive layer (i.e., Cu, etc.) on asubstrate is shown, according to one embodiment of the invention. Thevertical axis shows thickness 304 measured in Angstroms (A), while thehorizontal axis shows the voltage response (V) 302 as measured by theeddy current sensor. In this example, a higher response voltagecorrelates to a smaller thickness. Calibration curves may also becreated for the same purpose with the response voltage decreasing, e.g.,by offsetting each probe response voltage by its maximum voltageobtained in the system with no film to be measured.

In a simplified example, at a particular substrate temperature, thereported eddy current response V (voltage), with reasonable proximitycorrection properties, may be modeled as:2V=R _(I)(d,ρ _(I))+R _(II)(d,ρ _(II))≈R _(I)(d, ρ _(I))+ε_(p) ·dR _(I)/dp+R _(II)(d, ρ _(II))−ε_(p) ·dR _(II) /dp   [EQUATION 6]where if ε_(p) is the proximity variation from ρ_(I) at the actual timeof the measurement for sensor I, then, inferring from the fixed geometrybetween sensor I and sensor II, −ε_(p) is the proximity variation fromp_(II), at the actual time of the measurement for sensor II if and onlyif the measurement from sensor II is made simultaneously. For purposesof this example, the sensor serial number S is assumed to be the samefor all sensors, only d and p will be considered for purposes of thecalculations. In addition, although the responses are shown in voltage,other electrical characteristics such as current may be used as well.

Both sensors are assumed have a substantially identical response attheir nominal proximity R(d,p_(I))=R(d,p_(II)) to film thickness. Inpractice, this can be reasonably done mechanically as mentioned below orwith sensor dependent correlation functions. In addition, the responsesensitivity for both sensors to proximity variation (e.g., proximityelectrical response) is also assumed to be the same in magnitude.Subsequently, dR_(I)/dp evaluated at p_(I) equals dR_(II)/dp evaluatedat p_(II) and the proximity dependent terms in EQUATION 6 cancel out andprovide a proximity independent measurement which can be correlated withthe film thickness.

In an embodiment, this may be accomplished by using a set of pairedsensors of substantially the same type (hence about same performance)and loading the substrate halfway between them. Subsequently, the filmmay have the same nominal proximity to both sensors. Therefore,canceling out terms, the simplified reported measurement can be shown tobe:2V=2R(d)+0   [EQUATION 7]

which may be independent of small proximity variations. In a simplifiedexample, for a single sensor, if R_(I)(d,p_(I))=R_(I)(d,p_(I))=1.5V, andif dR_(I)/dp=2V/mm, ε_(p)=0.1 mm, then:2V=R _(I)(d,p _(I))+ε_(p) ·dR _(I) /dp+R _(II)(d,p _(I))−ε_(p) ·dR _(II)/dp=1.5V+2V/nm*0.1 mm+1.5V−2V/nm*0.1 mm=3V   [EQUATION 8]

Thus in an ideal simultaneous measurement situation this method yieldsabout 0% in proximity error or typically about 3α<0.03V. It should beclear that these analyses may be carried out with appropriate changes inweighting proportion between the two sensors in the sum in order toensure cancellation of the relevant proximity terms or to include morethan two sensors, but the fundamental properties described remain.

However, it may not be practical to measure the substrate at thecalibration temperature. For example, a substrate process may requirethat the substrate be heated to a temperature substantially above thecalibration temperature. Subsequently waiting for the substrate to cooldown, just to take a set of measurements, may result in substantiallydecreased production throughput. However, temperature may affect theunderlying resistivity of a conductive film, and hence affects themeasured eddy current response.

Referring now to FIG. 4, a simplified diagram of a substrate with aconductive film comprising Cu, cycled between about 21° C. and about 23°C. across 200 minutes, according to an embodiment of the invention. Thehorizontal axis 406 represents time in minutes, the left-hand verticalaxis 402 represents substrate temperature in degrees (° C), whileright-hand vertical axis 404 represents conductive film thickness inangstroms (Å) reported by the eddy current system. Plot 408 representschange in substrate and film temperature over about the 200 minuteinterval, while plot 410 shows the corresponding change in the reportedconductive film thickness measured by the eddy current system. In thisexample, Cu has a temperature coefficient (α) of 0.0035/degC. Assubstrate temperature 408 moves in one direction, increasing ordecreasing, the corresponding conductive film thickness (as measured byeddy current response) moves in the opposite direction. For example, atabout 60 minutes (412), the substrate temperature is about 21.58° C.,while the corresponding conductive film thickness is about 9536 Å.However, at about 68 minutes, the substrate temperature is about 22.10°C., while the corresponding conductive film thickness is about 21.68 Å.

Referring now to FIG. 5, a simplified diagram of a substrate with aconductive film comprising Si, cycled between about 21° C. and about 23°C. across 200 minutes, according to an embodiment of the invention. Thehorizontal axis 506 represents time in minutes, the left-hand verticalaxis 502 represents substrate temperature in degrees (° C), whileright-hand vertical axis 504 represents conductive film thickness inangstroms (Å). Plot 508 represents change in substrate temperature overabout the 200 minute interval, while plot 510 shows the correspondingchange in measured conductive film thickness. In this example, Si has atemperature coefficient (α) of −0.011/degC. As substrate temperature 508moves in one direction, increasing or decreasing, the correspondingconductive film thickness (as measured by eddy current response) movesin the opposite direction. For example, at about 60 minutes (512), thesubstrate temperature is about 21.63° C., while the correspondingconductive film thickness is about 14.15 Å. However, at about 68minutes, the substrate temperature is about 22.12° C., while thecorresponding conductive film thickness is about 13.1 Å.

Subsequently, if the change in resistivity is proportional to acorresponding change in temperature for a given material as some giventemperature range, then a change in the resistivity of a conductivelayer on a substrate due to a change temperature in that temperaturerange may be modeled as:ρ(T _(c)+τ)=ρ(T _(c))(1+α(τ−T _(c)))   [EQUATION 9]where ρ (T_(c)) is the resistivity in ohm meters of the conductive filmat the calibration temperature (calibration resistivity), τ is thetemperature deviation of the target substrate from the calibrationtemperature, and α is the temperature coefficient for the conductivefilm in degC⁻¹. Typical values of α are: for Cu about +0.0039 to about0.0068 degC⁻¹, for Si about −0.07 to about −0.01 degC⁻¹, and can belooked up or measured as described below for most materials of interest

Subsequently, for relatively small changes in temperature, the resultingchange in the measured conductive film thickness may be substantiallydirectly proportional to the measured resistivity ρ(T_(m)), andsubstantially inversely proportional to the calibration resistivityρ(T_(c)). Thus, EQUATION 3 may be further simplified as: $\begin{matrix}{d_{m} = {\frac{\rho\left( T_{c} \right)}{\rho\left( T_{m} \right)}{f\left( {R\left( {d_{a},p,{\rho\left( T_{c} \right)}} \right)} \right.}}} & \left\lbrack {{EQUATION}\quad 10} \right\rbrack\end{matrix}$where, d_(m) is the conductive film thickness derived from the eddycurrent response measurement, d_(a) is the actual conductive filmthickness, T_(c) is the calibration temperature, T_(m) is the substratetemperature of the measured eddy current response of interest(measurement temperature), f(R(d_(a), p, ρ(T_(c))) is the conductivefilm thickness at the calibration temperature T_(c), p is the sensorproximity to the conductive film, ρ(T_(c)) is resistivity of theconductive film at the calibration temperature T_(c) (calibrationresistivity), ρ(T_(m)) is resistivity of the conductive film at themeasurement temperature T_(m) (measured resistivity).

Substituting EQUATION 9 into EQUATION 10: $\begin{matrix}{d_{m} = {\frac{f\left( {R\left( {d_{a},p,{\rho\left( T_{c} \right)}} \right)} \right)}{\left( {1 + {\alpha\left( {\tau - T_{c}} \right)}} \right)} = \frac{f\left( R_{c} \right)}{\left( {1 + {{\alpha\Delta}\quad T}} \right)}}} & \left\lbrack {{EQUATION}\quad 11} \right\rbrack\end{matrix}$

where, f(R(d, p, ρ(T_(c)))) or f(R_(c)) is the thickness of theconductive film on the substrate at the calibration temperature, τ−T_(c)or ΔT is the difference in temperature between the calibrationtemperature and the temperature at which the eddy current was measured,and α is the temperature coefficient for the conductive film in degC⁻¹.For a small (αΔT)² product (e.g., ≈0.0), EQUATION 11 can be furthersimplified to: $\begin{matrix}{d = {{\frac{f\left( R_{c} \right)}{\left( {1 + {{\alpha\Delta}\quad T}} \right)}\frac{\left( {1 - {{\alpha\Delta}\quad T}} \right)}{\left( {1 - {{\alpha\Delta}\quad T}} \right)}} = {\frac{{{f\left( R_{c} \right)} - {{f\left( R_{c} \right)}\alpha\quad\Delta\quad T}}\quad}{1 - \left( {\alpha\quad\Delta\quad T} \right)^{2}} \approx {{f\left( R_{c} \right)} - {{f\left( R_{c} \right)}{\alpha\Delta}\quad T}}}}} & \left\lbrack {{EQUATION}\quad 12} \right\rbrack\end{matrix}$

Subsequently, small eddy current perturbations caused by temperature maybe detected. For example, for a conductive film comprised of Cu, aperturbation of about 0.4% of the total may be measured. In addition,this perturbation may be measured independently of sensor proximity p.For example, proximity variations may be cancelled out by techniques,such as using a set of paired sensors of substantially the same type andloading the substrate halfway between them, as previously described.

In an embodiment, an electrical response of a reference substrate at aknown temperature may be used to correct the electrical response of atarget substrate at an unknown temperature. That is, for a referencesubstrate and a target substrate at a substantially similar but unknowntemperature, but which have substantially the same resistivity responseto a temperature change, and a set of set of calibration curves for thereference substrate at a known temperature, the resistivity correctionρ(T_(c))/ρ(T_(m)) for the target substrate may be determined bycombining EQUATION 3 and EQUATION 10 as follows: $\begin{matrix}{d_{c - {ref}} = {f\left( {R\left( {d_{a},p,{\rho\left( T_{c} \right)}} \right)} \right)}} & \left\lbrack {{EQUATION}\quad 13} \right\rbrack \\{d_{m - {ref}} = {{f\left( {R\left( {d,p,{\rho\left( T_{m} \right)}} \right)} \right)} = {\frac{\rho\left( T_{c} \right)}{\rho\left( T_{m} \right)}d_{c - {ref}}}}} & \left\lbrack {{EQUATION}\quad 14} \right\rbrack\end{matrix}$where, d_(c−ref) is the measured conductive film thickness on thereference substrate at the calibration temperature, which is generallyequal to the actual conductive film thickness d_(a), and d_(m−ref) isthe measured conductive film thickness on the reference substrate at themeasurement temperature, ρ(T_(c)) is the resistivity of the referencesubstrate at the calibration temperature T_(c), and ρ(T_(m)) is theresistivity of the reference substrate at a measured temperature T_(m),which is also substantially similar to the resistivity of the targetsubstrate at the same temperature.

Subsequently, assuming a reference substrate is configured to have asubstantially similar eddy current response as a target substrate, thena change in the reference conductive film thickness between acalibration and measurement temperature (auto compensation factor) maybe used to correct the eddy current response of the target substrate.Thus, EQUATION 14 may be rewritten as: $\begin{matrix}{d_{m - {tar}} = {\frac{\mathbb{d}_{c - {ref}}}{\mathbb{d}_{m - {ref}}}\frac{\rho\left( T_{c} \right)}{\rho\left( T_{m} \right)}{f\left( {R\left( {d,p} \right)} \right)}}} & \left\lbrack {{EQUATION}\quad 15} \right\rbrack\end{matrix}$where, η is an auto compensation factor d_(c−ref)/d_(m−ref), d_(c−ref)is the measured conductive film thickness on the reference substrate atthe calibration temperature, d_(m−ref) is the measured conductive filmthickness on the reference substrate at the measurement temperature,ρ(T_(c)) is the resistivity of the reference substrate at thecalibration temperature T_(c) and ρ(T_(m)) is the resistivity of thereference substrate at a measured temperature T_(m), and, since we'veexplicitly modeled the resistivity dependence as shown in EQUATION 10,f(R(d,p)) is a function of conductive film thickness that is independentof temperature. Substituting for η: $\begin{matrix}{d_{m - {tar}} = {\frac{\mathbb{d}_{c - {ref}}}{\mathbb{d}_{m - {ref}}}\frac{\rho\left( T_{c} \right)}{\rho\left( T_{m} \right)}{f\left( {R\left( {d,p} \right)} \right)}}} & \left\lbrack {{EQUATION}\quad 16} \right\rbrack\end{matrix}$

Substituting EQUATION 14 into EQUATION 16: $\begin{matrix}{d = {{\frac{\mathbb{d}_{c - {ref}}}{\left( \frac{{\rho\left( T_{c} \right)}\mathbb{d}_{c - {ref}}}{\rho\left( T_{m} \right)} \right)}\frac{\rho\left( T_{c} \right)}{\rho\left( T_{m} \right)}{f\left( {R\left( {d,p} \right)} \right)}} = {f\left( {R\left( {d,p} \right)} \right)}}} & \left\lbrack {{EQUATION}\quad 17} \right\rbrack\end{matrix}$

In an embodiment, d_(m−ref) of the reference substrate may be measuredby an eddy current sensor prior to measuring d_(m-tar) of the targetsubstrate. In an embodiment, d_(m−ref) of the reference substrate may bemeasured by an eddy current sensor after measuring d_(m−tar) of thetarget substrate or the average of the before and after d_(m−ref)measurements may be used to minimize errors due to temperature driftsduring measurement of multiple target sites on the substrate. Aspreviously stated, and in general, measured conductive film thickness isrelated to conductive film temperature. Hence, in environments where thetemperature may be changing, a good approximation of the referencesubstrate conductive film thickness d_(m−ref), at least for purposes ofcalculation, may be derived by averaging a d_(m−ref) taken before themeasurement of d_(m−tar), to a d_(m−ref) taken after. In an embodiment,the reference substrate is a small landing pad of known Cu conductivefilm thickness that is positioned relative to one or more positions neara given point on the substrate to be measured.

In an embodiment, the thickness of a target conductive film on asubstrate with a plurality of conductive films may be may be determined.In general, a measured eddy current response on a substrate includes theaggregate responses of all conductive films on that substrate. However,for a set of conductive films, each with a different resistivity p withrespect to temperature, a particular conductive film eddy currentresponse may be isolated by measuring the aggregate eddy currentresponse at n different temperatures, where n is the number ofconductive films on the substrate. In practice the behavior of the filmstack to small changes in ΔT can be described by an effectivetemperature coefficient α_(eff). The same auto compensation factorapproach may then be used since it does not depend on the knowledge ofthe numerical value of the temperature coefficient, but only that thereference sample behave like the target wafer.

Referring now to FIG. 6, a simplified diagram comparing temperaturecoefficient α to substrate mean thickness for a conductive filmsubstantially comprising Cu, according to one embodiment of theinvention. The horizontal axis 606 shows the measured substrate meanconductive film thickness in Angstroms (Å). Left vertical axis 602 showseffective temperature coefficient (α) of the substrate with film stack.The horizontal line 610 shows the nominal value of the temperaturecoefficient 0.0035/degC for Cu. The curve 612 shows the variation ineffective alpha for the substrate with film stack. Right vertical axis604 shows reduction in 3σ variability in Angstroms (Å). That is, theimprovement in eddy current reported thickness repeatability caused bycorrection of 2-3° C. variation in room temperature. This improvement isshown as point plots 608.

In general, above a certain threshold, as the eddy current response dueto that target film increases (e.g. a thicker conductive film), theeffective temperature coefficient (α) of a conductive film, shown by612, approaches the nominal temperature coefficient (α) for thatconductive film, shown by 610. Hence, only a relatively small number ofreference samples may be required to calibrate the eddy current responseto a measured conductive film thickness. The actual number of referencesamples will generally depend on the precision of the temperaturecompensation desired, as well as the thickness range of the targetconductive film. For example, the temperature compensation for copperfilms less than −4000Å, at 614, may be quite small and could be ignored,while for copper films greater than −4000Å significant improvement couldbe obtained with a single reference sample with copper thickness in therange of 10,000 Å. The selection of the appropriate correctioncoefficient within the small number of reference samples may be based onthe estimate of the target film thickness from the uncorrected firstmeasurements of the target film.

As was previously mentioned, in general, a measured eddy currentresponse on a substrate includes the aggregate responses of allconductive films on that substrate. However, for a set of conductivefilms, each with a different resistivity ρ with respect to temperature,a particular conductive film eddy current response may be isolated bymeasuring the aggregate eddy current response at n differenttemperatures, where n is the number of conductive films on thesubstrate. If the conductive films have different temperaturecoefficients, this knowledge may be used to differentiate the portion ofthe eddy current measurement caused by different films. For example, asubstrate with two conductive films (i.e., Cu, Si, etc.) may be measuredat two different temperatures, in order to substantially isolate andthus determine the eddy current response attributed to one of theconductive films.

Subsequently, at any given temperature T, a substrate with twoconductive films may be modeled as:V=R(d _(A-CF1),p, ρ_(CF1)(T _(m)))+βR(d _(A-CF2), p, ρ_(CF2)(T _(m)))  [EQUATION 18]where d_(A-CF1) is the actual thickness of a first conductive film onthe reference substrate, d_(A-CF2) is the actual thickness of a secondconductive film on the reference substrate, p is the sensor proximity tothe conductive film, ρ_(CF1) (T) is resistivity of the first conductivefilm at a temperature T, ρ_(CF2) (T) is resistivity of the secondconductive film at the temperature T, β is a conductive film thicknessdependent ratio (e.g., to account for conductive film 3-d effects suchas very thick copper dominating the temperature behavior on Sisubstrates as shown in the previous figure), and V is eddy currentresponse in volts.

Substituting, EQUATION 14 into EQUATION 18, $\begin{matrix}{V = {{\frac{\rho_{{CF}\quad 1}\left( T_{c} \right)}{\rho_{{CF}\quad 1}\left( T_{m} \right)}R_{c - {{CF}\quad 1}}} + {\frac{\rho_{{CF}\quad 2}\left( T_{c} \right)}{\rho_{{CF}\quad 2}\left( T_{m} \right)}\beta\quad R_{c - {{CF}\quad 2}}}}} & \left\lbrack {{EQUATION}\quad 19} \right\rbrack\end{matrix}$where T_(m) is the temperature at which the eddy current response ismeasured, T_(c) is the calibration temperature, ρ_(CF1)() is resistivityof the first conductive film, ρ_(CF2)() is resistivity of the secondconductive film, R_(-CF1) is the eddy current response of the firstconductive film at the calibration temperature, R_(c-CF2) is the eddycurrent response of the second conductive film at the calibrationtemperature, β is a conductive film thickness dependent ratio, and V iseddy current response in volts. Thus, for a substrate with twoconductive films at a given temperature, there are generally twounknowns, R_(c-CF1) and βR_(c-CF2).

However, if the aggregate eddy current response of a substrate with twoconductive films is generally measured at least at two differenttemperatures, the eddy current response of an individual conductive filmmay be determined. For example, EQUATION 19 may be re-written for twoaggregate eddy current measurements taken at two different temperaturesas:V ₁ =B ₁ R _(c-CF1) +C ₁ βR _(c-CF2)   [EQUATION 20]V ₂ =B ₂ R _(c-CF1) +C ₂ βR _(c-CF2)   [EQUATION 21]where, B₁=ρ_(CF1)(T_(c))/ρ_(CF1)(T₁), B₂=ρ_(CF1)(T_(c))/ρ_(CF1)(T₂),C₁=ρ_(CF2)(T_(c))/ρ_(CF2)(T₁), C₂=ρ_(CF2)(T_(c))/ρ_(CF2)(T₂).

As commonly understood in the art, EQUATION 20 and EQUATION 21 can befurther simplified using Cramer's Rule: $\begin{matrix}{R_{c - {{CF}\quad 1}} = {\frac{\begin{matrix}V_{1} & C_{1} \\V_{2} & {C_{2}\quad}\end{matrix}}{\begin{matrix}B_{1} & C_{1} \\B_{2} & {C_{2}\quad}\end{matrix}} = \frac{\left( {{V_{1}C_{2}} - {V_{2}C_{1}}} \right)}{\left( {{B_{1}C_{2}} - {B_{2}C_{1}}} \right)}}} & \left\lbrack {{EQUATION}\quad 22} \right\rbrack \\{{\beta\quad R_{c - {{CF}\quad 2}}} = {\frac{\begin{matrix}V_{1} & B_{1} \\V_{2} & {B_{2}\quad}\end{matrix}}{\begin{matrix}C_{1} & B_{1} \\C_{2} & {B_{2}\quad}\end{matrix}} = \frac{\left( {{V_{1}B_{2}} - {V_{2}B_{1}}} \right)}{\left( {{C_{1}B_{2}} - {C_{2}B_{1}}} \right)}}} & \left\lbrack {{EQUATION}\quad 23} \right\rbrack\end{matrix}$

For demonstration, this equation can be further simplified in the casein which one of the eddy current response measurements is taken at thecalibration temperature. For example, if T₁ is the calibrationtemperature (e.g. T_(c)=T₁), EQUATION 20 and EQUATION 21 can berewritten as follows:V ₁ =R _(c-CF1) +βR _(c-CF2)   [EQUATION 24]V ₂ =B ₂ R _(c-CF1) +C ₂ βR _(c-CF2)   [EQUATION 25]where, B₂=ρ_(CF1)(T_(c))/ρ_(CF1)(T₂)=(1+α_(CF1)ΔT₂)⁻¹, andC₂=ρ_(CF2)(T_(c))/ρ_(CF2)(T₂)=(1+α_(CF2)ΔT₂)⁻¹.

Again, as commonly understood in the art, EQUATION 24 and EQUATION 25can be further simplified using Cramer's Rule: $\begin{matrix}{R_{c - {{CF}\quad 1}} = {\frac{\begin{matrix}V_{1} & 1 \\V_{2} & {C_{2}\quad}\end{matrix}}{\begin{matrix}1 & 1 \\B_{2} & {C_{2}\quad}\end{matrix}} = \frac{\left( {{V_{1}C_{2}} - V_{2}} \right)}{\left( {C_{2} - B_{2}} \right)}}} & \left\lbrack {{EQUATION}\quad 26} \right\rbrack\end{matrix}$ $\begin{matrix}{{\beta\quad R_{c - {{CF}\quad 2}}} = {\frac{\begin{matrix}V_{1} & B_{1} \\V_{2} & {B_{2}\quad}\end{matrix}}{\begin{matrix}C_{1} & B_{1} \\C_{2} & {B_{2}\quad}\end{matrix}} = \frac{\left( {{V_{1}B_{2}} - V_{2}} \right)}{\left( {B_{2} - C_{2}} \right)}}} & \left\lbrack {{EQUATION}\quad 27} \right\rbrack\end{matrix}$

Expanding, for example, the denominator of EQUATION 26: $\begin{matrix}{R_{c - {{CF}\quad 1}} = \frac{{V_{1}\left( {1 + {\alpha_{{CF}\quad 2}\Delta\quad T_{2}}} \right)}^{- 1} - V_{2}}{\left( {1 + {\alpha_{{CF}\quad 2}\Delta\quad T_{2}}} \right)^{- 1} - \left( {1 + {\alpha_{{CF}\quad 1}\Delta\quad T_{2}}} \right)^{- 1}}} & \left\lbrack {{EQUATION}\quad 28} \right\rbrack\end{matrix}$

Further simplifying EQUATION 26: $\begin{matrix}{R_{c - {{CF}\quad 1}} = {\frac{{V_{1}\left( {1 + {\alpha_{{CF}\quad 2}\Delta\quad T_{2}}} \right)}^{- 1} - V_{2}}{\left( {1 + {\alpha_{{CF}\quad 2}\Delta\quad T_{2}}} \right)^{- 1} - \left( {1 + {\alpha_{{CF}\quad 1}\Delta\quad T_{2}}} \right)^{- 1}}\frac{\left( {1 + {\alpha_{{CF}\quad 2}\Delta\quad T_{2}}} \right)}{\left( {1 + {\alpha_{{CF}\quad 2}\Delta\quad T_{2}}} \right)}}} & \left\lbrack {{EQUATION}\quad 29} \right\rbrack \\{R_{c - {{CF}\quad 1}} = \frac{V_{1} - {V_{2}\left( {1 + {\alpha_{{CF}\quad 2}\Delta\quad T_{2}}} \right)}}{1 - \frac{\left( {1 + {\alpha_{{CF}\quad 2}\Delta\quad T_{2}}} \right)}{\left( {1 + {\alpha_{{CF}\quad 1}\Delta\quad T_{2}}} \right)}}} & \left\lbrack {{EQUATION}\quad 30} \right\rbrack\end{matrix}$where R_(c-CF1) is the eddy current response of the first conductivefilm at the calibration temperature, α_(CF1) is the temperaturecoefficient for the first conductive film in degC⁻¹, α_(CF2) is thetemperature coefficient for the second conductive film in degC⁻¹, ΔT₂ isthe difference between the calibration temperature T_(c) and themeasured temperature T₂, V₁ is the aggregate eddy current response atthe calibration temperature T_(c), and V₂ is the aggregate eddy currentresponse at the measured temperature T₂. Note that if one is onlyinterested in conductive film 1, no knowledge of the relativecontribution of the two films (i.e., β, etc.) is required. One may nowconstruct the normal correlation functions based off of R_(c-CF1) as thesubstrate and temperature independent eddy current response and thusreport an improved eddy current result such as CF1 film thickness.

Likewise, the eddy current response for R_(c-CF2) may be shown as$\begin{matrix}{{\beta\quad R_{c - {{CF}\quad 2}}} = \frac{{V_{2}\left( {1 + {\alpha_{{CF}\quad 2}\Delta\quad T_{2}}} \right)} - V_{1}}{\frac{\left( {1 + {\alpha_{{CF}\quad 2}\Delta\quad T_{2}}} \right)}{\left( {1 + {\alpha_{{CF}\quad 1}\Delta\quad T_{2}}} \right)} - 1}} & \left\lbrack {{EQUATION}\quad 31} \right\rbrack\end{matrix}$again where R_(c-CF2) is the eddy current response of the secondconductive film at the calibration temperature, β is a conductive filmthickness dependent ratio, α_(CF1) is the temperature coefficient forthe first conductive film in degC⁻¹, α_(CF2) is the temperaturecoefficient for the second conductive film in degC⁻¹, ΔT₂ is thedifference between the calibration temperature T_(c) and the measuredtemperature T₂, V₁ is the aggregate eddy current response at thecalibration temperature T_(c), and V₂ is the aggregate eddy currentresponse at the measured temperature T₂ If both film signals are desiredacross significant differences in film thickness, one may constructwafers to measure the relative contributions to the eddy currentmeasurements as for the film stacks of interest. For example in the casewhere a copper film (CF1=copper) is primarily varying across some rangeof thicknesses, one may determine β(d_(c-CF1)) over the range ofinterest and use the correlation results based on EQUATION 30 todetermine an eddy current response R_(c-CF2) normalized across variousfilm thicknesses by dividing EQUATION 31 by β(d_(c-CF1))

Referring now to FIG. 7, a simplified method of determining a thicknessof a first conductive layer on a target substrate, the target substratefurther having a second conductive layer is shown, according on anembodiment of the invention. Initially, at step 702, a first eddycurrent sensor is positioned at a given position relative to the targetsubstrate. Next, at step 704, a set of sensor electrical responses ismeasured at a first target substrate temperature. Next, at step 706, asecond set of electrical responses measured at a second target substratetemperature different from the first target substrate temperature. Next,at step 708, a third set of electrical responses is calculated using atleast the first and second set of electrical responses, and atemperature coefficient of a first conductive layer. Finally, at step710, the first thickness is determined from the third set of electricalresponses.

While this invention has been described in terms of several preferredembodiments, there are alterations, permutations, and equivalents whichfall within the scope of this invention. It should also be noted thatthere are many alternative ways of implementing the methods of thepresent invention. In addition, the invention is not limited to aparticular sensor design, method of detection, excitation frequency,active or passive electrical components or any other peculiarities of asensor vendor's method of reporting a sensible signal to be measured.Also, more than two sensors may be used. Furthermore, the term set asused herein includes one or more of the named element of the set. Forexample, a set of “X” refers to one or more “X.”

Advantages of the invention include methods and apparatus for optimizingan electrical response to a set of conductive layers on a substrate.Additional advantages include the use of relatively inexpensiveequipment to refine proximity correction, and higher substratemeasurement throughput.

Having disclosed exemplary embodiments and the best mode, modificationsand variations may be made to the disclosed embodiments while remainingwithin the subject and spirit of the invention as defined by thefollowing claims.

1. A method of determining a first thickness of a first conductive layerformed of a first conductive material on a target substrate, said targetsubstrate further having a second conductive layer formed of a secondconductive material different from said first conductive material,comprising: positioning a first eddy current sensor at a given positionrelative to said target substrate, said first eddy current sensor beingin a spaced-apart relationship with respect to said target substratewhen positioned at said given position; measuring, using said first eddycurrent sensor while said first eddy current sensor is positioned atsaid given position, a first set of electrical responses that includesat least one of a first voltage measurement and a first currentmeasurement, said measuring said first set of electrical responses beingperformed at a first target substrate temperature; measuring, using saidfirst eddy current sensor while said first eddy current sensor ispositioned at said given position, a second set of electrical responsesthat includes at least one of a second voltage measurement and a secondcurrent measurement, said measuring said second set of electricalresponses being performed at a second target substrate temperaturedifferent from said first target substrate temperature; calculating athird set of electrical responses using at least said first set ofelectrical responses and said second set of electrical responses, and afirst temperature coefficient of said first conductive layer, said thirdset of electrical responses representing responses substantiallyattributable to said first conductive layer; and determining said firstthickness from said third set of electrical responses.
 2. The method ofclaim 1 wherein said target substrate has N conductive layersaltogether, whereby N is an integer, said determining said firstthickness of said first conductive layer involving making at least Nmeasurements at N different temperatures.
 3. The method of claim 1wherein said third set of electrical responses is calculated based on:$R_{c - {{CF}\quad 1}} = \frac{V_{1} - {V_{2}\left( {1 + {\alpha_{{CF}\quad 2}\Delta\quad T_{2}}} \right)}}{1 - \frac{\left( {1 + {\alpha_{{CF}\quad 2}\Delta\quad T_{2}}} \right)}{\left( {1 + {\alpha_{{CF}\quad 1}\Delta\quad T_{2}}} \right)}}$where R_(c-CF1) is the eddy current response of the first conductivefilm at the calibration temperature, α_(CF1) is the temperaturecoefficient for the first conductive film in degC⁻¹, α_(CF2) is thetemperature coefficient for the second conductive film in degC⁻¹, ΔT₂ isthe difference between the calibration temperature T_(c) and themeasured temperature T₂, V₁ is the aggregate eddy current response atthe calibration temperature T_(c), and V₂ is the aggregate eddy currentresponse at the measured temperature T₂.
 4. The method of claim 3wherein said determining said first thickness includes correlating saidthird set of electrical responses with said first thickness using a setof thickness correlation curves.
 5. The method of claim 3 wherein saidset of thickness correlation curves are calculated using a mathematicaloptimization function that relates a thickness of said first conductivelayer with a plurality of electrical responses computed to besubstantially attributable to said first conductive layer.
 6. The methodof claim 1 wherein said first conductive layer comprises at least one ofaluminum, copper, and tungsten.
 7. The method of claim 1 wherein saidfirst set of electrical responses represents a set of electricalresponses that has been corrected for proximity variation between saidfirst eddy current sensor and said target substrate.
 8. An arrangementfor determining a first thickness of a first conductive layer formed ofa first conductive material on a target substrate, said target substratefurther having a second conductive layer formed of a second conductivematerial different from said first conductive material, comprising: aneddy current sensor disposed at a given position relative to said targetsubstrate, said first eddy current sensor being in a spaced-apartrelationship with respect to said target substrate when said first eddycurrent sensor is positioned at said given position; means for storing afirst set of electrical responses, said first set of electricalresponses being measured using said first eddy current sensor while saidfirst eddy current sensor is positioned at said given position, saidfirst set of electrical responses being measured at a first targetsubstrate temperature; means for storing a second set of electricalresponses, said second set of electrical responses being measured usingsaid first eddy current sensor while said first eddy current sensor ispositioned at said given position, said second set of electricalresponses being measured at a second target substrate temperaturedifferent from said first target substrate temperature; means forcalculating a third set of electrical responses using at least saidfirst set of electrical responses and said second set of electricalresponses, and a first temperature coefficient of said first conductivelayer, said third set of electrical responses representing responsessubstantially attributable to said first conductive layer; and means fordetermining said first thickness from said third set of electricalresponses.
 9. The arrangement of claim 8 wherein said target substratehas N conductive layers altogether, whereby N is an integer, saiddetermining said first thickness of said first conductive layerinvolving making at least N measurements at N different temperatures.10. The arrangement of claim 8 wherein said third set of electricalresponses is calculated based on:$R_{c - {{CF}\quad 1}} = \frac{V_{1} - {V_{2}\left( {1 + {\alpha_{{CF}\quad 2}\Delta\quad T_{2}}} \right)}}{1 - \frac{\left( {1 + {\alpha_{{CF}\quad 2}\Delta\quad T_{2}}} \right)}{\left( {1 + {\alpha_{{CF}\quad 1}\Delta\quad T_{2}}} \right)}}$where R_(c-CF1) is the eddy current response of the first conductivefilm at the calibration temperature, α_(CF1) is the temperaturecoefficient for the first conductive film in degC⁻¹, α_(CF2) is thetemperature coefficient for the second conductive film in degC⁻¹, ΔT₂ isthe difference between the calibration temperature T_(c) and themeasured temperature T₂, V₁ is the aggregate eddy current response atthe calibration temperature T_(c), and V₂ is the aggregate eddy currentresponse at the measured temperature T₂.
 11. The arrangement of claim 10wherein said means for determining said first thickness includes meansfor correlating said third set of electrical responses with said firstthickness using a set of thickness correlation curves.
 12. Thearrangement of claim 10 wherein said set of thickness correlation curvesare calculated using a mathematical optimization function that relates athickness of said first conductive layer with a plurality of electricalresponses computed to be substantially attributable to said firstconductive layer.
 13. The arrangement of claim 8 wherein said firstconductive layer comprises at least one of aluminum and copper.
 14. Amethod of determining a first thickness of a first conductive layerformed of a first conductive material on a target substrate, said targetsubstrate further having at least a second conductive layer formed of asecond conductive material different from said first conductivematerial, comprising: measuring, using an eddy current sensor disposedproximate to said target substrate, at least two sets of electricalresponses at two different target substrate temperatures; calculating alayer-specific set of electrical responses from said at least two setsof electrical responses, said layer-specific set of electricalresponses, said layer-specific set of electrical responses representingresponses substantially attributable to said first conductive layer; anddetermining said thickness from said layer-specific set of electricalresponses.
 15. The method of claim 14 wherein said target substrate hasN conductive layers altogether, whereby N is an integer, saiddetermining said first thickness of said first conductive layerinvolving making at least N measurements at N different temperatures.16. The method of claim 14 wherein said determining said thickness fromsaid layer-specific set of electrical responses is calculated based on$R_{c - {{CF}\quad 1}} = \frac{V_{1} - {V_{2}\left( {1 + {\alpha_{{CF}\quad 2}\Delta\quad T_{2}}} \right)}}{1 - \frac{\left( {1 + {\alpha_{{CF}\quad 2}\Delta\quad T_{2}}} \right)}{\left( {1 + {\alpha_{{CF}\quad 1}\Delta\quad T_{2}}} \right)}}$where R_(c-CF1) is the eddy current response of the first conductivefilm at the calibration temperature, α_(CF1) is the temperaturecoefficient for the first conductive film in degC⁻¹, α_(CF2) is thetemperature coefficient for the second conductive film in degC⁻¹, ΔT₂ isthe difference between the calibration temperature T_(c) and themeasured temperature T₂, V₁ is the aggregate eddy current response atthe calibration temperature T_(c), and V₂ is the aggregate eddy currentresponse at the measured temperature T₂.
 17. The method of claim 16wherein said determining said thickness from said layer-specific set ofelectrical responses includes using a set of thickness correlationcurves.
 18. The method of claim 17 wherein said set of thicknesscorrelation curves are calculated using a mathematical optimizationfunction that relates a thickness of said first conductive layer with aplurality of electrical responses computed to be substantiallyattributable to said first conductive layer.
 19. The method of claim 16wherein said first conductive layer comprises at least one of aluminumand copper.
 20. The method of claim 16 wherein said measuring, using aneddy current sensor disposed proximate to said substrate, at least twosets of electrical responses at two different target substratetemperatures represents a set of electrical responses that has beencorrected for proximity variation between said first eddy current sensorand said target substrate.